Who vs Whom

Hi Greedypigeon , welcome to GMAT Club.

The subject is not whom.
Whom is the object of the preposition OF.
The object of a preposition is never the subject of a clause.

The subject of that clause is both.

We will see phrases such as some of whom, many of whom, none of whom, or both of whom,
all of which are very common phrase structures in English (I just used one).

Jargon: the pronouns some, many, none and both are called "indefinite pronouns."

The construction of this type of phrase that refers to people is this way:
indefinite pronoun + of + OBJECT pronoun (

Subject pronouns: I, you, he, she, it, we, they
Object pronouns: me, you, him, her, it, us, them, whom

We should think both of whom = both of them
Them is never a subject. Them go to the store. ouch.
Them doesn't actively do anything, ever.

Indefinite pronouns such as both are still pronouns and thus able to function as a subject in the same way that a noun would.

Hope that helps.